A counterexample on overtaking optimality

Mathematical Methods of Operations Research

Volumn 49, Issue 3, 1999, Pages 435-439

  Nowak, Andrzej S ^a   Vega Amaya, Oscar ^b  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b UNIVERSIDAD DE SONORA   (Mexico)

Author keywords

Markov decision chains; Overtaking optimality criteria

Indexed keywords

EID: 0040024227     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001860050059     Document Type: Article

References (18)

1. Altman E, Hordijk A, Spieksma FM (1997) Contraction conditions for average and α-discount optimality in countable state Markov games with unbounded rewards. Math. Oper. Res. 22:588-618
2. Arapostathis A, Borkar VS, Fernnández-Gaucherand E, Ghosh MK, Marcus SI (1993) Discrete-time controlled Markov processes with average cost criterion: a survey. SIAM. J. Control Optim. 31:282-344
3. Brown BW (1965) On the iterative method of dynamic programming on a finite space discrete time Markov processes. Ann. Math. Statist. 36:1279-1285
4. Dekker R, Hordijk A (1992) Recurrence conditions for average and Blackwell optimality in denumerable state Markov decision chains. Math. Oper. Res. 17:271-289
5. Denardo EV, Rothblum UG (1979) Overtaking optimality for Markov decision chains. Math. Oper. Res. 4:144-152
6. Denardo EV, Miller BL (1968) An optimality condition for discrete dynamic programming with no discounting. Ann. Math. Statist. 39:1220-1227
7. Dutta PK (1991) What do discounted optima converge to? A theory of discount rate asymptotics in economic models. J. Economic Theory 55:64-94
8. Fernnández-Gaucherand E, Ghosh MK, Marcus SI (1994) Controlled Markov processes on the infinite planning horizon: weighted and overtaking cost criteria. Math. Methods of Oper. Res. 39:131-155
9. Gale D (1967) On optimal development in a multisector economy. Rev. Econ. Studies 34:1-19
10. Gordienko E, Hernández-Lerma O (1995) Average cost Markov control processes with weighted norms: existence of canonical policies. Applicationes Mathematicae 23:199-218
11. Hernández-Lerma O, Lasserre JB (1996) Discrete-time Markov control processes: Basic optimality criteria. Springer-Verlag, New York
12. Hernández-Lerma O, Vega-Amaya O (1998) Infinite horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality. Applicationes Mathematicae 25:153-178
13. Leizarowitz A (1987) Infinite horizon optimization for finite state Markov chain. SIAM J. Control Optim. 25:1601-1618
14. Leizarowitz A (1996) Overtaking and almost-sure optimality for infinite horizon Markov decision processes. Math. Oper. Res. 21:158-181
15. Nowak AS (1999) Optimal strategies in a class of zero-sum ergodic stochastic games. Math. Meth. Oper. Res. 50, forthcoming
16. Puterman ML (1994) Markov decision processes. Wiley, New York
17. Ramsey FP (1928) A mathematical theory of savings. Economic J. 38:543-559
18. von Weizsäcker CC (1965) Existence of optimal programs of accumulation for an infinite horizon. Review of Econom. Studies 32:85-104